There are 20 questions on a multiple-choice test. Each question has 4 possible answers. If a student takes the quiz unprepared and guesses the answers. What is the probability that he does not answer any question correctly? What is the probability that he gets four questions correct? What is the probability that he gets four or five questions correct? What is the probability that he gets four or fewer questions correct? What is the probability that he gets five or more questions correct? How many questions can he expect to get right? What is the variance of the number of questions he can expect to get right?